Semi-heuristic parameter choice rules for Tikhonov regularisation with operator perturbations

DOI10.1515/jiip-2018-0062zbMath1490.65110arXiv1807.05042OpenAlexW2963812766MaRDI QIDQ2633409

Stefan Kindermann, Uno Hämarik, Urve Kangro, Kemal Raik

Publication date: 8 May 2019

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.05042

zbMATH Keywords

inverse problemsill-posed problemsregularisationoperator perturbationsparameter choice rules

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60) Perturbation theory of linear operators (47A55) Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (3)

A numerical comparison of some heuristic stopping rules for nonlinear Landweber iteration ⋮ Unnamed Item ⋮ A new heuristic parameter choice rule in Tikhonov regularization applied for Ritz approximation of an ill-posed problem

Uses Software

• Regularization tools

Cites Work

• Unnamed Item
• Unnamed Item
• On the quasi-optimal rules for the choice of the regularization parameter in case of a noisy operator
• Comparison of parameter choices in regularization algorithms in case of different information about noise level
• Comparing parameter choice methods for regularization of ill-posed problems
• On the generalized discrepancy principle for Tikhonov regularization in Hilbert scales
• On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization
• Regularization of ill-posed problems by stochastic iteration procedures in the mean
• Regularization methods for large-scale problems
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems
• On Minimization Strategies for Choice of the Regularization Parameter in Ill-Posed Problems
• Regularization of linear ill-posed problems with noisy right hand side and noisy operator
• Regularized Total Least Squares: Computational Aspects and Error Bounds
• Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion
• Heuristic Parameter Choice in Tikhonov Method from Minimizers of the Quasi-Optimality Function
• The quasi-optimality criterion in the linear functional strategy
• A General Heuristic for Choosing the Regularization Parameter in Ill-Posed Problems

This page was built for publication: Semi-heuristic parameter choice rules for Tikhonov regularisation with operator perturbations